In this paper we deal with a feedback control design for the action potential of a neuronal membrane in relation with the non-linear dynamics of the Hodgkin-Huxley mathematical model. More exactly, by using an external current as a control expressed by a relay graph in the equation of the potential, we aim at forcing it to reach a certain manifold in finite time and to slide on it after that. From the mathematical point of view we solve a system involving a parabolic differential inclusion and three nonlinear differential equations via an approximating technique and a fixed point result. The existence of the sliding mode and the determination of the time at which the potential reaches the prescribed manifold are proved by a maximum principle argument. Numerical simulations are presented.
Sliding mode control of the Hodgkin-Huxley mathematical model / C. Cavaterra, G. Marinoschi, D. Enachescu. - In: EVOLUTION EQUATIONS AND CONTROL THEORY. - ISSN 2163-2480. - 8:4(2019), pp. 883-902.
|Titolo:||Sliding mode control of the Hodgkin-Huxley mathematical model|
|Parole Chiave:||Hodgkin–Huxley model; sliding mode control; feedback stabilization; nonlinear parabolic equations; reaction-diffusion systems|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2019|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.3934/eect.2019043|
|Appare nelle tipologie:||01 - Articolo su periodico|